Bias versus variance when fitting multi-species molecular lines with a non-LTE radiative transfer model: Application to the estimation of the gas temperature and volume density
Artikel i vetenskaplig tidskrift, 2024

Context. Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines. Aims. We study several hypotheses that enable robust estimations of the column densities and physical conditions when fitting one or two transitions per molecular species. We study the extent to which simplifying assumptions aimed at reducing the complexity of the problem introduce estimation biases and how to detect them. Methods. We focus on the CO and HCO+ isotopologues and analyze maps of a 50 square arcminutes field. We used the RADEX escape probability model to solve the statistical equilibrium equations and compute the emerging line profiles, assuming that all species coexist. Depending on the considered set of species, we also fixed the abundance ratio between some species and explored different values. We proposed a maximum likelihood estimator to infer the physical conditions and considered the effect of both the thermal noise and calibration uncertainty. We analyzed any potential biases induced by model misspecifications by comparing the results on the actual data for several sets of species and confirmed with Monte Carlo simulations. The variance of the estimations and the efficiency of the estimator were studied based on the Cramér-Rao lower bound. Results. Column densities can be estimated with 30% accuracy, while the best estimations of the volume density are found to be within a factor of two. Under the chosen model framework, the peak 12CO (1 -0) is useful for constraining the kinetic temperature. The thermal pressure is better and more robustly estimated than the volume density and kinetic temperature separately. Analyzing CO and HCO+ isotopologues and fitting the full line profile are recommended practices with respect to detecting possible biases. Conclusions. Combining a non-local thermodynamic equilibrium model with a rigorous analysis of the accuracy allows us to obtain an efficient estimator and identify where the model is misspecified. We note that other combinations of molecular lines could be studied in the future.

Methods: statistical

Methods: data analysis

Line: profiles

ISM: general

Radiative transfer

ISM: clouds


Antoine Roueff

Université de Toulon

J. Pety

Institut de Radioastronomie Millimétrique (IRAM)

Observatoire de Paris

M. Gerin

Observatoire de Paris

L. Segal

Université de Toulon

Institut de Radioastronomie Millimétrique (IRAM)

J.R. Goicoechea

CSIC - Instituto de Fisica Fundamental (IFF)

Harvey Liszt

National Radio Astronomy Observatory

P. Gratier

Laboratoire d'Astrophysique de Bordeaux

Ivana Bešlić

Observatoire de Paris

Lucas Einig

Université Grenoble Alpes

Institut de Radioastronomie Millimétrique (IRAM)

Mathilde Gaudel

Observatoire de Paris

Jan Orkisz

Chalmers, Rymd-, geo- och miljövetenskap, Astronomi och plasmafysik

Pierre Palud

Observatoire de Paris

Université de Lille

Miriam G. Santa-Maria

CSIC - Instituto de Fisica Fundamental (IFF)

Victor De Souza Magalhaes

Institut de Radioastronomie Millimétrique (IRAM)

Antoine Zakardjian

Institut de Recherche en Astrophysique et Planétologie (IRAP)

Sébastien Bardeau

Institut de Radioastronomie Millimétrique (IRAM)

E. Bron

Observatoire de Paris

Pierre Chainais

Université de Lille

Simon Coudé

Environment Environment

Harvard-Smithsonian Center for Astrophysics

K. Demyk

Institut de Recherche en Astrophysique et Planétologie (IRAP)

Viviana Guzman

Pontificia Universidad Catolica de Chile

A. Hughes

Institut de Recherche en Astrophysique et Planétologie (IRAP)

David Languignon

Observatoire de Paris

F. Levrier

Laboratoire de Physique de l’Ecole Normale Supérieure

D. C. Lis

California Institute of Technology (Caltech)

Jacques Le Bourlot

Observatoire de Paris

Franck Le Petit

Observatoire de Paris

Nicolas Peretto

Cardiff University

Evelyne Roueff

Observatoire de Paris

A. Sievers

Institut de Radioastronomie Millimétrique (IRAM)

Pierre Antoine Thouvenin

Université de Lille

Astronomy and Astrophysics

0004-6361 (ISSN) 1432-0746 (eISSN)

Vol. 686 A255


Astronomi, astrofysik och kosmologi

Atom- och molekylfysik och optik

Sannolikhetsteori och statistik



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